symmetry group of regular hexagon

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people dihedral group
gptkbp:actsOn	regular hexagon
gptkbp:automorphismGroup	regular hexagon
gptkbp:containsElement	12
gptkbp:hasReflection	reflection over axis through midpoints of opposite edges reflection over axis through opposite vertices
gptkbp:hasReflectionSymmetries	6
gptkbp:hasRotation	rotation by 0° rotation by 120° rotation by 180° rotation by 240° rotation by 300° rotation by 60°
gptkbp:hasRotationalSymmetries	6
gptkbp:hasSubgroup	gptkb:Klein_four-group gptkb:cyclic_group_of_order_6 cyclic group of order 2 cyclic group of order 3
https://www.w3.org/2000/01/rdf-schema#label	symmetry group of regular hexagon
gptkbp:identityElement	identity transformation
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	gptkb:D6
gptkbp:name	gptkb:dihedral_group_of_order_12
gptkbp:order	12
gptkbp:presentedBy	⟨r, s \| r^6 = s^2 = 1, s r s = r^{-1}⟩
gptkbp:symbol	gptkb:D6
gptkbp:usedIn	gptkb:geometry crystallography group theory
gptkbp:bfsParent	gptkb:dihedral_group_of_order_12
gptkbp:bfsLayer	7